Systems and methods for determining compensated conductivities

ABSTRACT

The disclosed systems and methods determine compensation factors, compensated conductivities, concentrations, and other related parameters of a solution based on the solution&#39;s temperature and absolute conductivity.

BACKGROUND

Solutions in which a chemical is dissolved in water are commonlyreferred to as aqueous solutions. Some aqueous solutions conductelectricity; this property is referred to as conductivity. Theconductivity of an aqueous solution depends on the solution'sconcentration, which is a ratio between the amounts of chemical andwater in the solution, and the solution's temperature.

The conductivities of some concentrations of some species (i.e.,chemical types) of aqueous solutions are well known. For example, theconductivities of many different concentrations of sulfuric acid havebeen measured at several temperatures by Darling and other researchers.These conductivities are often presented in the form of referenceconductivity curves. A reference conductivity curve shows therelationship between conductivity and concentration for a species ofaqueous solution at a reference temperature. FIG. 6 shows referenceconductivity curves for sulfuric acid at reference temperatures of 0°C., 18° C., or 25° C.

Since the conductivity of an aqueous solution depends on itsconcentration, a measurement of conductivity is often used to deduceconcentration. This measurement is compensated for temperature byscaling it to the conductivity that the solution would have if thetemperature of the solution were brought to the reference temperature ofa reference conductivity curve for the species (e.g., 0° C., 18° C., or25° C. for the curves for sulfuric acid shown in FIG. 6). This scalingdepends solely on temperature and results in a compensated conductivity.The compensated conductivity is then compared to the referenceconductivity curve, and the concentration of the solution is determinedto be the reference concentration whose reference conductivity mostclosely approaches the compensated conductivity.

The ratio between absolute conductivity and compensated conductivity isusually referred to as the temperature compensation factor. Thetemperature compensation factor for most species of aqueous solutionsdepends relatively strongly on temperature and relatively weakly onconcentration. As such, computing the temperature compensation factorbased solely on temperature, but not on concentration, is sufficient forordinary applications, e.g., applications that do not require highdegrees of accuracy. (In other words, assuming that differentconcentrations of a solution have the same temperature compensationfactor is usually a sufficient approximation for ordinary applications.)Computing the temperature compensation factor based solely ontemperature is not sufficient, though, for applications that requirehigh degrees of accuracy.

Unfortunately, while a solution's temperature can be measured prior tocompensating the solution's conductivity, the solution's concentrationcannot be determined until after compensation. Present scenarios fordetermining compensated conductivities, compensation factors,concentrations, and other related solution parameters have, therefore,limited accuracy.

SUMMARY

Generally, the disclosed systems and methods can determine a temperaturecompensation factor for a solution based on the solution's temperatureand absolute conductivity, rather than just the solution's temperature.The disclosed systems and methods facilitate increased accuracydeterminations of compensation factors, compensated conductivities,concentrations, and other related solution parameters. The disclosedsystems and methods can be applied to aqueous solutions (e.g., solutionsin which one or more chemicals are dissolved in water) and non-aqueoussolutions (e.g., solutions in which one or more chemicals are dissolvedin a solvent that includes a non-water component).

Methods for determining concentrations and other related solutionparameters are described. In embodiments, reference conductivities ofreference concentrations of a solution at a reference temperature areprovided. Based on the solution's temperature and conductivity, aconversion factor for converting the conductivity to a compensatedconductivity at the reference temperature is determined. Based on theconversion factor and the conductivity, the compensated conductivity ofthe solution is computed. The concentration is then determined based onthe compensated conductivity, the reference conductivities, and thereference concentrations.

In one embodiment, pre-determined conversion factors that are associatedwith conductivities and temperatures are provided and the conversionfactor is determined based on the pre-determined conversion factor thatis associated with the solution's conductivity and temperature.Alternatively, the conversion factor is determined based oninterpolating between pre-determined conversion factors. Thepre-determined conversion factors may be provided in a look-up table.

In one embodiment, an expression for the conversion factor is providedand the conversion factor is determined based on computing a value ofthe expression for the solution's conductivity and temperature.

In some embodiments, the expression is generated based on the followingscenario. The conductivities of a group of different concentrations ofthe solution are provided at the reference temperature and non-referencetemperatures. For each non-reference temperature and each differentconcentration in the group, a ratio is determined between theconductivity of the concentration at the non-reference temperature andthe conductivity of the concentration at the reference temperature (orvice-versa). A relationship is then determined among the ratios, theconductivities of the different concentrations, and the temperature.

In an embodiment, the compensated conductivity is computed based on aproduct of the conductivity and the conversion factor or its reciprocal.

In embodiments, the methods further include calibrating the conductivityprior to determining the conversion factor. In one aspect, a conversionfactor for converting a reference conductivity of the solution at areference temperature to an estimated conductivity of the solution at asolution temperature is determined. An estimated conductivity at thesolution temperature is computed based on the reference conductivity andthe conversion factor. The conductivity is then calibrated based on ameasure of the difference between the conductivity and the estimatedconductivity.

Devices for determining chemical concentrations and other relatedsolution parameters are also described. In embodiments, the devicesinclude digital data processing devices that are in communication withthe reference data for the solution and that are configured to executefeatures of the previously described methods.

Processor-readable mediums including instructions for determiningchemical concentrations and other related solution parameters are alsodescribed. The processor-readable mediums include instructions to causea processor to execute features of the previously described methods.

Systems for determining chemical concentrations and other relatedsolution parameters are also described. In embodiments, the systemsinclude a temperature sensor, a conductivity sensor, a digital dataprocessing device in communication with the temperature and conductivitysensors, and a medium that can be read by the digital data processingdevice and that includes reference data and instructions for causing thedigital data processing device to execute features of the previouslydescribed methods. In some embodiments, the systems further include adisplay and/or an alarm in communication with the digital dataprocessing device.

These and other features of the disclosed systems and methods can bemore fully understood by referring to the following detailed descriptionand accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart that illustrates an exemplary method fordetermining a concentration of a solution;

FIG. 2 is a flow chart that illustrates an exemplary method fordetermining a temperature compensation factor of a solution;

FIGS. 3 and 4 are flow diagrams that illustrate some features of theflow elements in the flow chart of FIG. 2;

FIG. 5 schematically illustrates an exemplary system for determining aconcentration of a solution; and,

FIG. 6 shows reference conductivity curves for sulfuric acid.

DESCRIPTION

Illustrative embodiments will now be described to provide an overallunderstanding of the disclosed systems and methods. One or more examplesof the illustrative embodiments are shown in the drawings. Those ofordinary skill in the art will understand that the disclosed systems andmethods can be adapted and modified to provide systems and methods forother applications, and that other additions and modifications can bemade to the disclosed systems and methods without departing from thescope of the present disclosure. For example, features of theillustrative embodiments can be combined, separated, interchanged,and/or rearranged to generate other embodiments. Such modifications andvariations are intended to be included within the scope of the presentdisclosure.

FIG. 1 is a flow chart that illustrates an exemplary method forcomputing a concentration of a solution. As will be understood by thoseof ordinary skill in the art, the disclosed systems and methods are notlimited to the flow elements shown in FIG. 1 and can compute aconcentration of a solution based on one or more flow elements that aredifferent than and/or additional to those shown in FIG. 1.

As shown in FIG. 1, the temperature, conductivity, and species of asolution are determined, measured, or otherwise provided based onschemes known to those of ordinary skill in the art (110 in FIG. 1).This conductivity is usually referred to as the absolute conductivity ofthe solution. For example, the temperature and absolute conductivity canbe measured using well known sensors. In most embodiments, the speciesis known a priori. In some embodiments, however, the species may bedetermined using filter paper or other well known techniques. Referenceconductivities and reference concentrations of the species at areference temperature are also provided (120 in FIG. 1). Such referencedata may be provided in the form of a reference conductivity curve forthe species, similar to one of the curves shown in FIG. 6. Alternativelyor in combination, such reference data may be provided in another form,such as in one or more data structures, e.g., look-up tables.

As also shown in FIG. 1, a temperature compensation factor forconverting the absolute conductivity of the solution at the solution'stemperature to a compensated conductivity of the solution at thereference temperature is then determined based on the solution'stemperature and absolute conductivity (130 in FIG. 1). For reference,the temperature compensation factor is referred to herein as aconversion factor.

In most embodiments, the conversion factor is determined by computing avalue of an expression that was previously deduced from empirical datafor the species of the solution and that represents the factor as afunction of solution temperature and absolute conductivity. Schemes forgenerating the expression are described further herein with respect toFIGS. 2–4.

Alternatively, in some embodiments, the conversion factor is determinedby referring to one or more data structures (e.g., look-up tables) thatinclude pre-determined conversion factors that are indexed to and/orotherwise associated with solution temperatures and absoluteconductivities. In some embodiments, the pre-determined conversionfactors may simply be empirical measurements of those factors, e.g.,measurements of the ratios and other data in FIG. 2 (220). Alternativelyand/or in combination, in some embodiments, the pre-determinedconversion factors may be computed values of the above expression. In atleast some of the foregoing types of embodiments, determining theconversion factor includes determining whether one of the pre-determinedconversion factors is associated with the solution's temperature andabsolute conductivity. If one of the pre-determined conversion factorsis so associated, then the conversion factor for the solution isdetermined to be the one of the pre-determined conversion factors. Ifnone of the pre-determined conversion factors is so associated, however,then the conversion factor is determined based on interpolating betweenpre-determined conversion factors.

As further shown in FIG. 1, the compensated conductivity is thencomputed based on the absolute conductivity and the conversion factor(140 in FIG. 1). In most embodiments, the conversion factor is a ratiobetween absolute conductivity and compensated conductivity, and thecompensated conductivity is computed based on the product of theabsolute conductivity and the reciprocal of the conversion factor. Insome embodiments, the conversion factor is a ratio between compensatedconductivity and absolute conductivity, and the compensated conductivityis computed based on the product of the absolute conductivity and theconversion factor.

With continuing reference to FIG. 1, the concentration of the solutionis ultimately determined based on the compensated conductivity, thereference data, and schemes known to those of ordinary skill in the art(150 in FIG. 1). For example, in some embodiments, the concentration ofthe solution is determined to be that reference concentration whosereference conductivity is equal to, most nearly equal to, or otherwiseclosely approaches the compensated conductivity.

FIG. 2 is a flow chart that illustrates an exemplary method forgenerating an expression for the conversion factor, i.e., the factor forconverting the solution's absolute conductivity at the solution'stemperature to a compensated conductivity of the solution at thereference temperature. As previously described, in most embodiments, theflow elements of FIG. 2 are performed prior to the flow elements of FIG.1, so that the expression and/or computed values of the expression maybe used on “live” data in FIG. 1 (130). As will be understood by thoseof ordinary skill in the art, the disclosed systems and methods are notlimited to the flow elements shown in FIG. 2 and can compute aconversion factor based on one or more flow elements that are differentthan and/or additional to those shown in FIG. 1.

As shown in FIG. 2, empirical data for the species of the solution aredetermined, measured, or otherwise provided (210 in FIG. 2). Theempirical data include absolute conductivities of a group ofconcentrations of the species at (i) a temperature that will be selectedas the reference temperature and (ii) at least two other temperatures(and, in most embodiments, between ten and twenty temperatures) referredto as non-reference temperatures. For some species, the empirical datais available in one or more published reference sources known to thoseof ordinary skill in the art. (For example, the data for sulfuric acidshown in FIG. 6 is based on published data by Darling and otherresearchers.) For other species, the empirical data may be acquired bydirect measurement. The group of concentrations includes severaldifferent concentrations over a range of concentrations to allow thebehavior of absolute conductivity with concentration at the referencetemperature and each of the non-reference temperatures to be deducedwith a degree of certainty that is reasonable to one of ordinary skillin the art. While data at relatively few concentrations (e.g., five) maybe enough to deduce the behavior for some species at a giventemperature, data at relatively more concentrations (e.g., fifteen) maybe necessary to deduce the behavior of other species at the giventemperature.

As also shown in FIG. 2, based on the empirical data, ratios aredetermined between the conductivities at the non-reference temperaturesand the conductivities at the reference temperature (220 in FIG. 2).Generally, for each temperature in the empirical data (i.e., thereference temperature and each of the non-reference temperatures) andeach concentration in the empirical data, a ratio is determined betweenthe absolute conductivity of that concentration at that temperature andthe absolute conductivity of that concentration at the referencetemperature. In some embodiments, the reciprocal of this ratio isdetermined. Accordingly, a result is a set of ordered triplets for eachconcentration in the empirical data, namely, temperature, theconcentration's absolute conductivity at that temperature, and a ratiobetween the concentration's absolute conductivity at that temperatureand its absolute conductivity at the reference temperature. It can berecognized that this ratio is unity for the reference temperatureitself.

FIG. 3 schematically illustrates features of FIG. 2's ratiodetermination 220 for sulfuric acid at a reference temperature of 25° C.and non-reference temperatures of 0° C. and 18° C., based on the datashown in FIG. 6. As shown in FIG. 3, for each of 0° C., 18° C., and 25°C. and each concentration, a ratio is determined between theconductivity at 0°/18°/25° C. and the conductivity at 25° C.

With continuing reference to FIG. 2, a relationship is then determinedamong the temperatures x, the absolute conductivities y, and the ratiosz in the empirical data, to deduce an expression for the ratios z as afunction f of the temperatures x and the absolute conductivities y,wherez=f(x,y)(230 in FIG. 2). The deduced expression z is the conversion factor forconverting the absolute conductivity y of a solution at a solutiontemperature x to a compensated conductivity of the solution at thereference temperature.

FIG. 4 schematically illustrates features of FIG. 2's expressiondetermination 230 for sulfuric acid with a reference temperature of 25°C., where the values of x (° C.), y (Siemens/cm), and z (dimensionless)are based on Darling's empirical data. The expression for the ratio z isdetermined based on curve-fitting schemes known to those of ordinaryskill in the art. For example, in some embodiments, the expression isdetermined by providing the x, y, and z data to a software package (suchas a commercially available software packages) that can fit athree-dimensional function f to the data. One or more criteria may beconsidered in determining whether an expression proposed by the softwarepackage is a “good” fit to the data. Such criteria can include the valueof χ² or another criterion that quantifies the fit; the smoothness ofthe expression (relatively smooth expressions are preferable toexpressions with unrealistic discontinuities); whether the value of z atthe reference temperature remains near 1 in the expression; whether theexpression is reversible, so that y may be expressed in terms of x andz, to thereby facilitate calibration of measurements of y, as describedfurther below; the speed of computation with the expression; and/orother criteria that will be apparent to those of ordinary skill in theart.

As shown in the example embodiment of FIG. 4, the surface described bythe following ratio of simple, non-orthogonal polynomials:z=f(x,y)=(a+bx+cy)/(1+dx+ey)is a mathematically “good” fit to the data for sulfuric acid, where thecoefficients a, b, c, d, and e are floating point constantsa=0.72531379, b=0.01881595, c=−0.49131471, d=0.0076371079, ande=−0.48257362. The expression shown in FIG. 4 is intended to beillustrative and non-limiting; those of ordinary skill in the art willrecognize that other expressions (e.g., using non-simple and/ororthogonal polynomials) may be determined to be mathematically “good”fits to the empirical data under one or more criteria. Theaforementioned FIG. 4 expression represents the conversion factor forconverting the absolute conductivity y of a solution of sulfuric acid ata solution temperature x to a compensated conductivity y/z at areference temperature of 25° C. Since the conversion factor depends onthe solution's temperature and absolute conductivity, as opposed to onlythe solution's temperature as in present scenarios, the conversionfactor permits the conversion factor itself, compensated conductivities,concentrations, and other related solution parameters to be determinedwith increased accuracy.

As an illustrative and non-limiting example of the accuracy of thedisclosed systems and methods, consider two cases for sulfuric acid: (i)a first case in which solution temperature is 95° C. and absoluteconductivity is 0.25 S/cm; and, (ii) a second case in which solutiontemperature is still 95° C., but absolute conductivity is 1.25 S/cm.Using the expression deduced above for sulfuric acid at a referencetemperature of 25° C., the conversion factor for the first case iscomputed to be 1.489, while the conversion factor for the second case is1.692. The difference between these factors is about 13%. In contrast tothe disclosed systems and methods, present scenarios that computeconversion factors based solely on temperature predict the same factorfor both cases.

As will be understood by those of ordinary skill in the art, theexpression for the conversion factor that is deduced in FIG. 2 (230) isapplicable to a single reference temperature, i.e., that temperature inthe empirical data that is designated as the reference temperature(210). The expression cannot, therefore, be used for computations thatinvolve a different reference temperature.

In some embodiments, the expression, i.e., the function f, including itsform and the values of its coefficients (230) is stored for subsequentretrieval to determine a conversion factor (e.g., 130 in FIG. 1, 240 inFIG. 2).

Alternatively and/or in combination, in some embodiments, values of theexpression are computed for a variety of absolute conductivities andtemperatures (250 in FIG. 2) and stored in one or more data structures(e.g., look-up tables) for subsequent retrieval (e.g., 130 in FIG. 1,260 in FIG. 2).

The inverse of the expression deduced in FIG. 2 (230) may be used tocalibrate the absolute conductivity y of the solution (i.e.,measurements of absolute conductivity y, FIG. 1 (110) and/or FIG. 2(210)). In some embodiments, the absolute conductivity can be calibratedbased on the following scheme. The absolute conductivity y of a knownconcentration of a solution of a given species is measured at a solutiontemperature x, and the compensated conductivity s=y/z of theconcentration at a reference temperature is determined from a referenceconductivity curve for the solution. Applying the compensatedconductivity s=y/z and the solution temperature x to the inverse of theexpression results in a predicted absolute conductivity y of thesolution. The inverse can thus be understood as a conversion factor forconverting the reference conductivity at a reference temperature to anestimated absolute conductivity at the solution temperature. Forexample, the inverse of FIG. 4's expression for sulfuric acid is thequadratic equation:ey ² +y(1+dx−cs)−s(a+bx)=0,where a, b, c, d, and e are constant coefficients, y is the predictedabsolute conductivity, x is the solution temperature, and s is thecompensated conductivity. The non-negative y solution to this equationis the predicted conductivity for the solution. The measurements ofabsolute conductivity can then be calibrated based on a measure of thedifference (e.g., a difference, a root-mean-square difference, etc.)between the measured absolute conductivity and the predicted absoluteconductivity.

FIG. 5 schematically illustrates an exemplary system 500 for determininga chemical concentration of a solution 505 that is disposed in acontainer 507. As shown in FIG. 5, the system 500 includes a probe 510having sensors 512 and 514 for sensing the solution's temperature andconductivity, a digital data processing device 520 that is incommunication with the probe 510, a display 530 in communication withthe digital data processing device 520, a medium 540 (e.g., a memory)that can be accessed and/or read by the digital data processing device520 and that includes reference data and instructions that cause thedigital data processing device 520 to execute one or more of thepreviously described methods, and a user interface 550 in communicationwith the digital data processing device 520.

The sensors 512 and 514 may include sensors for detecting temperatureand conductivity that are known to those of ordinary skill in the art.While the sensors 512 and 515 are shown as being disposed on singleprobe 510 in the embodiment of FIG. 5, the sensors 512 and 514 may bedisposed on different probes in other embodiments.

The digital data processing device 520 is a processor-controlled devicethat is capable of receiving, processing, and/or transmitting digitaldata. It may include a personal computer (PC), a computer workstation(e.g., those manufactured by Sun or Hewlett-Packard), a laptop computer,a notebook computer, a server computer, a mainframe computer, a handhelddevice (e.g., a Pocket PC®), an information appliance, and/or anothertype of generic or special-purpose, processor-controlled device. Aprocessor refers to the logic circuitry that responds to processesinstructions that drive digital data processing devices and includes acentral processing unit, an arithmetic logic unit, an applicationspecific integrated circuit, a task engine, and/or combinations,arrangements, or multiples thereof.

The display 530 is a processor-controlled device that can visiblyproject at least numbers onto a display screen based on one or moreprojection schemes known to those of ordinary skill in the art. Forexample, the display may include a cathode ray tube, a liquid crystaldisplay, a display based on light-emitting diodes, and a display basedon a gas plasma.

The medium 540 is a processor-readable medium known to those of ordinaryskill in the art, e.g., compact disk (CD), digital video disk (DVD),magnetic tape or disk, internal hard drive, external hard drive, randomaccess memory (RAM), read-only memory (ROM), redundant array ofindependent disks (RAID), removable memory device, and/or anycombination of the foregoing.

The user 550 interface includes a processor-controlled input device forinteracting with a user. For example, the user interface may include amouse, a keyboard, a touch sensitive screen, a track ball, a keypad, astylus, and other input devices known to those of ordinary skill in theart.

In the shown embodiment, the digital data processing device 520, thedisplay 530, the medium 540, and the user interface 550 are housed in anintegrated unit 560 that includes a probe interface 518. Alternatively,one or more of these components may be housed separately from the othercomponents and/or may be located remotely (e.g., across a network, suchas LAN) from the other components.

In some embodiments, the system 500 may be packaged as an industrialprocess variable transmitter such as the INVENSYS®/FOXBORO® Model 875ECIntelligent Electrochemical Analyzer for Electrodeless ConductivityMeasurements, and/or may include features that are similar to theINVENSYS®/FOXBORO® Model 875EC Intelligent Electrochemical Analyzer forElectrodeless Conductivity Measurements. The system 500 can include atwo wire or a four wire configuration, or other configurations.

In most embodiments, medium 540 includes reference data and conversionfactors for several different species of solution and several differentreference temperatures, so that system 500 can be used by a user todetermine concentrations and other related parameters for a variety ofspecies of solution. The reference data includes the reference datadescribed with respect to flow FIG. 1 (120), and the conversion factorsinclude the expressions and/or the data structures (e.g., look-uptables) described with respect to flow FIG. 1 (130) and FIG. 2 (240,260).

As will be understood by those of ordinary skill in the art, thedisclosed systems and methods may be implemented without a display, suchas the display 530 shown in FIG. 5. For example, in some embodiments,the disclosed systems and methods may be implemented with an alarm thatis in communication with the digital data processing device 520. In onesuch embodiment, the digital data processing device 520 may activate thealarm (e.g., cause the alarm to emit a visible light signal and/or anaudible noise, etc.) based on one or more of the temperature, theabsolute conductivity, the conversion factor, the compensatedconductivity, and the concentration (e.g., based on a value of one ormore of the foregoing with respect to a pre-determined threshold). Alsofor example, in some embodiments, the digital data processing device 520may be configured so as to provide data representing one or more of thetemperature, the absolute conductivity, the conversion factor, thecompensated conductivity, and the concentration to another digital dataprocessing device (e.g., a device that controls system 500) via analogand/or digital telecommunications, industrial, and/or othercommunication standards and protocols.

An exemplary operation of system 500 will now be described. As will beunderstood by those of ordinary skill in the art, the disclosed systemsand methods are not limited to the exemplary operation and can beimplemented in operations that include features that are different thanand/or additional to those described herein.

A user desiring to compute one or more parameters of the solution 505determines the solution's species based on schemes known to those ofordinary skill in the art and provides an indication of that species(for example, sulfuric acid) to digital data processing device 520 viauser interface 550. (In some embodiments, the memory 540 may includeinstructions for causing the digital data processing device 520 todetermine that species.) The user then disposes the probe 510 and thesensors 512, 514 in the solution 505. Subsequently, the user and/orinstructions in memory 540 cause the digital data processing device 520to communicate with the sensors 512, 514, so as to determine thetemperature and the absolute conductivity of the solution 505. Thedigital data processing device 520 may provide the sensed temperatureand/or absolute conductivity to the display 530 for display thereon andobservation by the user. Subsequently, the digital data processingdevice 520 determines a conversion factor, a compensated conductivity, aconcentration, and/or another related parameter for the species ofsolution 505 based on reference data for the species and instructionsstored on memory 540. (In some embodiments, the digital data processingdevice 520 calibrates the absolute conductivity based on the previouslydescribed methods prior to computing the solution parameter.) Thedigital data processing device 520 may provide the computed parameter tothe display 530 for display thereon and observation thereby the user.

In some embodiments, the user specifies the parameter to be computed viathe user interface 550. Alternatively and/or in combination, in someembodiments, the digital data processing device 520 is pre-configured tocompute specific types of parameters.

Accordingly, systems and methods have been disclosed for determiningtemperature compensation factors based on solution temperature andabsolute conductivity. These temperature compensation factors facilitateincreased accuracy determinations of compensated conductivities,concentrations, and other related solution parameters.

The temperature compensation factors have been described as anintermediate in conversions from absolute conductivity to compensatedconductivity or in determinations of concentration. As will beunderstood by those of ordinary skill in the art, the temperaturecompensation factors may, in some embodiments, not ever be computed.Rather, the temperature and conductivity dependence of the temperaturecompensation factors may be embodied in the compensated conductivity,the concentration, and/or another related solution parameter. In someembodiments, therefore, the disclosed systems and methods may beimplemented so that the absolute conductivity is directly converted tocompensated conductivity and/or so that the concentration or otherrelated solution parameter is directly determined from absoluteconductivity, without computing a temperature compensation factor. Forexample, in some embodiments, the empirical data in FIG. 2 (210, 220)can be used to form a two-dimensional look-up table for converting theconductivity of the solution at the temperature to a compensatedconductivity of the solution at the reference temperature or aconcentration of the solution. The two-dimensional look-up tableincludes a first dimension for the solution's temperature and a seconddimension for the solution's absolute conductivity.

The systems and methods described herein are not limited to a hardwareor software configuration; they can find applicability in many computingor processing environments. The systems and methods can be implementedin hardware or software, or in a combination of hardware and software.The systems and methods can be implemented in one or more computerprograms, in which a computer program can be understood to comprise oneor more processor-executable instructions. The computer programs canexecute on one or more programmable processors, and can be stored on oneor more storage media readable by the processor, comprising volatile andnon-volatile memory and/or storage elements.

The computer programs can be implemented in high level procedural orobject oriented programming language to communicate with a computersystem. The computer programs can also be implemented in assembly ormachine language. The language can be compiled or interpreted. Thecomputer programs can be stored on a storage medium or a device (e.g.,compact disk (CD), digital video disk (DVD), magnetic tape or disk,internal hard drive, external hard drive, random access memory (RAM),redundant array of independent disks (RAID), or removable memory device)that is readable by a general or special purpose programmable computerfor configuring and operating the computer when the storage medium ordevice is read by the computer to perform the methods described herein.

Unless otherwise provided, references herein to memory can include oneor more processor-readable and -accessible memory elements and/orcomponents that can be internal to a processor-controlled device,external to a processor-controlled device, and/or can be accessed via awired or wireless network using one or more communications protocols,and, unless otherwise provided, can be arranged to include one or moreexternal and/or one or more internal memory devices, where such memorycan be contiguous and/or partitioned based on the application.

Unless otherwise provided, references herein to a/the processor anda/the microprocessor can be understood to include one or more processorsthat can communicate in stand-alone and/or distributed environment(s)and can be configured to communicate via wired and/or wirelesscommunications with one or more other processors, where such one or moreprocessor can be configured to operate on one or moreprocessor-controlled devices that can include similar or differentdevices. Use of such processor and microprocessor terminology can beunderstood to include a central processing unit, an arithmetic logicunit, an application-specific integrated circuit, and/or a task engine,with such examples provided for illustration and not limitation.

Unless otherwise provided, use of the articles “a” or “an” herein tomodify a noun can be understood to include one or more than one of themodified noun.

While the systems and methods described herein have been shown anddescribed with reference to the illustrated embodiments, those ofordinary skill in the art will recognize or be able to ascertain manyequivalents to the embodiments described herein by using no more thanroutine experimentation. Such equivalents are encompassed by the scopeof the present disclosure and the appended claims. Accordingly, thesystems and methods described herein are not to be limited to theembodiments described herein, can include practices other than thosedescribed, and are to be interpreted as broadly as allowed underprevailing law.

1. A method for determining a concentration of a solution based on aconductivity of the solution at a temperature, the method comprising:providing reference conductivities of reference concentrations of thesolution at a reference temperature, detecting the conductivity and thetemperature of the solution, based on the detected conductivity and thedetected temperature, determining a conversion factor for converting thedetected conductivity of the solution at the detected temperature to acompensated conductivity of the solution at the reference temperature,based on the detected conductivity and the conversion factor, computingthe compensated conductivity of the solution at the referencetemperature, based on the compensated conductivity, the referenceconductivities, and the reference concentrations, determining theconcentration of the solution, and outputting the concentration of thesolution.
 2. The method of claim 1, wherein determining the conversionfactor includes: providing pre-determined conversion factors that areassociated with conductivities and temperatures of the solution,determining the conversion factor based on the pre-determined conversionfactor that is associated with the detected conductivity and thedetected temperature of the solution.
 3. The method of claim 2, whereinproviding pre-determined conversion factors include: providing thepre-determined conversion factors in at least one look-up table.
 4. Themethod of claim 1, wherein determining the conversion factor includes:providing pre-determined conversion factors that are associated withconductivities and temperatures of the solution, determining whether oneof the pre-determined conversion factors is associated with the detectedconductivity and the detected temperature of the solution, based on oneof the pre-determined conversion factors being associated with thedetected conductivity and the detected temperature of the solution,determining the conversion factor to be the one of the pre-determinedconversion factors, and based on none of the pre-determined values beingassociated with the detected conductivity and the detected temperatureof the solution, determining the conversion factor based oninterpolating between pre-determined conversion factors.
 5. The methodof claim 1, wherein determining the conversion factor includes:providing an expression for the conversion factor based on temperatureand conductivity of the solution, and computing a value of theexpression for the detected conductivity and the detected temperature ofthe solution.
 6. The method of claim 5, wherein providing an expressionfor the conversion factor based on temperature and conductivity of thesolution includes: generating the expression for the solution.
 7. Themethod of claim 6, wherein generating the expression includes: at thereference temperature and non-reference temperatures, determining theconductivities of a group of different concentrations of the solution,for each non-reference temperature and each different concentration inthe group, determining the ratio of the conductivity of theconcentration at the non-reference temperature and the conductivity ofthe concentration at the reference temperature, and determining arelationship among the ratios, the conductivities of the differentconcentrations, and the temperatures.
 8. The method of claim 6, whereingenerating the expression includes: at the reference temperature andnon-reference temperatures, determining the conductivities of a group ofdifferent concentrations of the solution, for each non-referencetemperature and each different concentration in the group, determiningthe ratio of the conductivity of the concentration at the referencetemperature and the conductivity of the concentration at thenon-reference temperature, and determining a relationship among theratios, the conductivities, and the temperatures.
 9. The method of claim1, wherein computing the compensated conductivity of the solution at thereference temperature includes: generating the compensated conductivitybased on the product of the detected conductivity and the conversionfactor.
 10. The method of claim 1, wherein computing the compensatedconductivity of the solution at the reference temperature includes:generating the compensated conductivity based on the product of thedetected conductivity and the reciprocal of the conversion factor. 11.The method of claim 1, further comprising: prior to determining theconversion factor, calibrating the detected conductivity.
 12. The methodof claim 11, wherein calibrating includes: based on a referenceconductivity of the solution at a reference temperature, determining asecond conversion factor for converting the reference conductivity atthe reference temperature to an estimated conductivity at the detectedtemperature, based on the reference conductivity and the secondconversion factor, generating an estimated conductivity of the solutionat the detected temperature, and calibrating the conductivity based on ameasure of the difference between the detected conductivity and theestimated conductivity.
 13. A device for determining a concentration ofa solution based on a conductivity of the solution at a temperature, thedevice comprising: at least one digital data processing device receivinginputs of the conductivity and temperature of the solution and incommunication with reference conductivities of reference concentrationsof the solution at a reference temperature and configured for: based onthe conductivity and the temperature, determining a conversion factorfor converting the conductivity of the solution at the temperature to acompensated conductivity of the solution at the reference temperature,based on the conductivity and the conversion factor, computing thecompensated conductivity of the solution at the reference temperature,based on the compensated conductivity, the reference conductivities, andthe reference concentrations, determining the concentration of thesolution and outputting the concentration of the solution.
 14. Thedevice of claim 13, wherein the at least one digital data processingdevice is in communication with pre-determined conversion factors thatare associated with conductivities and temperatures of the solution andis configured for determining the conversion factor based on:determining whether one of the pre-determined conversion factors isassociated with the conductivity and the temperature of the solution,based on one of the pre-determined conversion factors being associatedwith the conductivity and the temperature of the solution, determiningthe conversion factor to be the one of the pre-determined conversionfactors, and based on none of the pre-determined values being associatedwith the conductivity and the temperature of the solution, determiningthe conversion factor based on interpolating between pre-determinedconversion factors.
 15. The device of claim 13, wherein the at least onedigital data processing device is in communication with an expressionfor the conversion factor based on temperature and conductivity of thesolution and is configured for determining the conversion factor basedon: computing a value of the expression for the conductivity and thetemperature of the solution.
 16. A processor-readable medium includinginstructions for determining a concentration of a solution based on aconductivity of the solution at a temperature and referenceconductivities of reference concentrations of the solution at areference temperature, the processor-readable medium includinginstructions to cause a processor to: receive inputs of the conductivityand temperature of the solution, based on the conductivity and thetemperature, determine a conversion factor for converting theconductivity of the solution at the temperature to a compensatedconductivity of the solution at the reference temperature, based on theconductivity and the conversion factor, compute the compensatedconductivity of the solution at the reference temperature, based on thecompensated conductivity, the at least one reference conductivity, andthe at least one reference concentration, determine the concentration ofthe solution, and output the concentration of the solution.
 17. Theprocessor-readable medium of claim 16, further including: pre-determinedconversion factors that are associated with conductivities andtemperatures of the solution, and instructions to cause the processorto: determine whether one of the pre-determined conversion factors isassociated with the conductivity and the temperature of the solution,based on one of the pre-determined conversion factors being associatedwith the conductivity and the temperature of the solution, determine theconversion factor to be the one of the pre-determined conversionfactors, and based on none of the pre-determined values being associatedwith the conductivity and the temperature of the solution, determine theconversion factor based on interpolating between pre-determinedconversion factors.
 18. The processor-readable medium of claim 16,further including: an expression for the conversion factor based ontemperature and conductivity of the solution, and instructions to causethe processor to compute a value of the expression for the conductivityand the temperature of the solution.
 19. A system for determining aconcentration of a solution, the system comprising: at least onetemperature sensor for detecting a temperature of the solution, at leaston conductivity sensor for detecting a conductivity of the solution, atleast one digital data processing device in communication with the atleast one temperature sensor and the at least one conductivity sensor,and at least one medium that is capable of being read by the at leastone digital data processing device and that includes: referenceconductivities of reference concentrations of the solution, andinstructions for causing the at least one digital data processing deviceto: based on the conductivity and the temperature, determine aconversion factor for converting the conductivity of the solution at thetemperature to a compensated conductivity of the solution at a referencetemperature, based on the conductivity and the conversion factor,compute the compensated conductivity of the solution at the referencetemperature, based on the compensated conductivity, the at least onereference conductivity, and the at least one reference concentration,determine the concentration of the solution.
 20. The system of claim 19,wherein the at least one medium further includes: pre-determinedconversion factors that are associated with conductivities andtemperatures of the solution, and instructions for causing the digitaldata processing device to: determine whether one of the pre-determinedconversion factors is associated with the conductivity and thetemperature of the solution, based on one of the pre-determinedconversion factors being associated with the conductivity and thetemperature of the solution, determine the conversion factor to be theone of the pre-determined conversion factors, and based on none of thepre-determined values being associated with the conductivity and thetemperature of the solution, determine the conversion factor based oninterpolating between pre-determined conversion factors.
 21. The systemof claim 19, wherein the at least one medium further includes: anexpression for the conversion factor based on temperature andconductivity of the solution, and instructions for causing the digitaldata processing device to compute a value of the expression for theconductivity and the temperature of the solution.
 22. The system ofclaim 19, further comprising: at least one display in communication withthe at least one digital data processing device, wherein the at leastone medium further includes instructions for causing the at least onedigital data processing device to provide data representing at least oneof the detected temperature, the detected conductivity, the compensatedconductivity, and the concentration to the display for display thereon.23. The system of claim 19, further comprising: at least one alarm incommunication with the at least one digital data processing device,wherein the at least one medium further includes instructions forcausing the at least one digital data processing device to activate theat least one alarm based on at least one of the detected temperature,the detected conductivity, the compensated conductivity, and theconcentration.
 24. The system of claim 19, wherein the at least onemedium further includes instructions for causing the at least onedigital data processing device to provide data representing at least oneof the detected temperature, the detected conductivity, the compensatedconductivity, and the concentration to a different digital dataprocessing device.
 25. A method for determining a compensatedconductivity of a solution at a reference temperature, the methodcomprising: detecting a conductivity and a temperature of the solution,based on the conductivity and the temperature, determining a conversionfactor for converting the conductivity of the solution at thetemperature to a compensated conductivity of the solution at thereference temperature, based on the conductivity and the conversionfactor, computing the compensated conductivity of the solution at thereference temperature, and outputting the compensated conductivity ofthe solution.
 26. A method for determining a compensated conductivity ofa solution at a reference temperature, the method comprising: detectinga conductivity and a temperature of the solution, providing at least onetwo-dimensional look-up table for converting the conductivity of thesolution at the temperature to a compensated conductivity of thesolution at the reference temperature, in which the two-dimensionallook-up table includes a first dimension for temperature and a seconddimension for conductivity, based on the two-dimensional look-up table,computing the compensated conductivity of the solution at the referencetemperature, and outputting the compensated conductivity of thesolution.
 27. A method for determining a concentration of a solution,the method comprising: providing at least one two-dimensional look-uptable of conversion factors for converting a conductivity of thesolution at a temperature to a concentration of the solution, in whichthe two-dimensional look-up table includes a first dimension fortemperature and a second dimension for conductivity, detecting theconductivity and the temperature of the solution, based on theconductivity and the temperature of the solution, determining acompensated conductivity at a reference temperature, based on aconversion factor determined from the at least one two-dimensionallook-up table for the compensated conductivity and the temperature,computing the concentration of the solution, and outputting theconcentration of the solution.